University of Kwazulu-Natal

Algebra 1 Unit 6 Lesson 2 Retrieval Problems Tutorial Open Up

Bonisiwe Shabane
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algebra 1 unit 6 lesson 2 retrieval problems tutorial open up

Rewrite each expression as the product of two binomials. Each expression involves two multiplication problems separated by a + or − sign. Each multiplication problem contains a matching binomial factor that can be factored out so that the expression becomes a product of two binomials. Factor out (4⁢x+1) and write the numbers that remain (3⁢x+2). In each set of three functions, one will be linear, one will be exponential, and one will be a quadratic function. Explain the nature of change for the function and find an explicit and recursive equation for each.

Graph the functions from the tables in problems 9 and 10. Add any additional characteristics you notice from the graph. Place the axes so that you can show all 5 points. Identify your scale. Write the explicit equation above the graph. In this unit, students study quadratic functions systematically.

They look at patterns which grow quadratically and contrast them with linear and exponential growth. Then they examine other quadratic relationships via tables, graphs, and equations, gaining appreciation for some of the special features of quadratic functions and the situations they represent. They analyze equivalent quadratic expressions and how these expressions help to reveal important behavior of the associated quadratic function and its graph. They gain an appreciation for the factored, standard, and vertex forms of a quadratic function and use these forms to solve problems. In this unit, students learn about quadratic functions. Earlier, they learned about linear functions that grow by repeatedly adding or subtracting the same amount and exponential functions that grow by repeatedly multiplying by the same amount.

Quadratic functions also change in a predictable way. Here, the number of small squares in each step is increasing by 3, then 5, then 7, and so on. How many squares are in Step 10? How many in Step \(n\)? In this unit, students will also learn about some real-world situations that can be modeled by quadratic functions. For example, when you toss a ball up in the air, its distance above the ground as time passes can be modeled by a quadratic function.

Study the graph. The ball starts on the ground because the height is 0 when time is 0. The ball lands back on the ground after 2 seconds. After 1 second, the ball is 5 meters in the air. Both of the following expressions give the ball’s distance above the ground: \(5x(2-x)\) and \(10x-5x^2\), where \(x\) represents the number of seconds since it was thrown. Quadratic expressions are most recognizable when you can see the “squared term,” \(\text-5x^2\), as shown in \(10x-5x^2\).

Your student will learn even more about quadratics in the next unit. Welcome to the IM® Grade 6 Algebra I Video Learning Series homepage. The 24 videos for each grade were selected to support fall-readiness for students as they prepare to enter the next grade in mathematics. While there are far more than 24 essential lessons at each grade, we identified key lessons aligned to major work of the grade that are necessary for students to find success in math at... A few things to note as you look through these videos:

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